Simplify the following expression: $\dfrac{44y^3}{12y^5}$ You can assume $y \neq 0$.
Solution: $ \dfrac{44y^3}{12y^5} = \dfrac{44}{12} \cdot \dfrac{y^3}{y^5} $ To simplify $\frac{44}{12}$ , find the greatest common factor (GCD) of $44$ and $12$ $44 = 2 \cdot 2 \cdot 11$ $12 = 2 \cdot 2 \cdot 3$ $ \mbox{GCD}(44, 12) = 2 \cdot 2 = 4 $ $ \dfrac{44}{12} \cdot \dfrac{y^3}{y^5} = \dfrac{4 \cdot 11}{4 \cdot 3} \cdot \dfrac{y^3}{y^5} $ $\phantom{ \dfrac{44}{12} \cdot \dfrac{3}{5}} = \dfrac{11}{3} \cdot \dfrac{y^3}{y^5} $ $ \dfrac{y^3}{y^5} = \dfrac{y \cdot y \cdot y}{y \cdot y \cdot y \cdot y \cdot y} = \dfrac{1}{y^2} $ $ \dfrac{11}{3} \cdot \dfrac{1}{y^2} = \dfrac{11}{3y^2} $